Regularized image restoration with singular value decomposition

In order to restore the degraded image caused by atmospheric turbulence, the two-dimensional degradation model is decomposed into a one-dimensional degradation model in the horizontal and vertical direction, respectively. First, a new regularizing filter function was proposed and the singular value decomposition is carried out for the fuzzy matrix of the one-dimensional degradation model. For the purpose of averting instability caused by smaller singular values in restoration, each singular value is multiplied by the corresponding new regularizing filter function value, So each degenerate column is restored in the vertical direction, and then the array is restored in the horizontal direction. Simulation shows that the algorithm achieved satisfactory results. By comparison with the recovery results with the truncated and the Tikhonov regularizing filter function, the new regularizing filter function is significantly better than the last two regularizing filter functions in both subjective visual and objective indexes.